for \(\rho \ge 1\) . Figure REF  shows a visualization of the Gumbel copula.
One can show that \(\lambda _U=2-2^{1/\theta }\)  [1]}. Figure REF  visualizes the Gumbel copula distribution with Gaussian and Gamma marginals. We can observe a decent dependency—indicated by the peak pointing to the upper right—in the upper-tail events, which is mathematically described by \(\lambda _U\) .

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